1st & 2nd Order Partial Derivatives

• December 3rd 2008, 07:03 AM
DirtMcGirt
1st & 2nd Order Partial Derivatives
Find the first and second order partial derivatives for the following function:

f(x,y) = 2x^3 - 6xy^2 +5y^4

Need to find:
fx
fy
fxx
fxy
fyx
fyy

I don't understand the concept of finding partial derivatives and my calculus text has (once again) proven itself to be worthless.

• December 3rd 2008, 07:33 AM
BoboStrategy
Re: Partial Derivatives
$f(x,y) = 2x^3 - 6xy^2 +5y^4$

When finding fx, variables other than x are treated as constants.

So $f_x = 6x^2 - 6y^2$

For $f_{xy}$ take the derivative of $f_x$ treating non-x variables as constants. $f_{xy} = 12y$
• December 3rd 2008, 07:47 AM
DirtMcGirt
2nd-Order
Are fxx and fyy just 2nd derivatives of fx and fy, respectively?

Are fxy and fyx always the same? I don't understand the difference between those two.